The graphs show the position $\mathrm { s }$, velocity $\mathrm { v } = \mathrm { ds } / \mathrm { dt }$, and acceleration $\mathrm { a } = \mathrm { d } ^ { 2 } \mathrm {~s} / \mathrm { dt } ^ { 2 }$ of a body moving along a coordinate line as functions of time $t$. Which graph is which?
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A) B = position, A = velocity, C = acceleration
B) C = position, A = velocity, B = acceleration
C) A = position, C = velocity, B = acceleration
D) A = position, B = velocity, C = acceleration

Question

The graphs show the position $\mathrm { s }$, velocity $\mathrm { v } = \mathrm { ds } / \mathrm { dt }$, and acceleration $\mathrm { a } = \mathrm { d } ^ { 2 } \mathrm {~s} / \mathrm { dt } ^ { 2 }$ of a body moving along a coordinate line as functions of time $t$. Which graph is which?
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A) B = position, A = velocity, C = acceleration 
B) C = position, A = velocity, B = acceleration 
C) A = position, C = velocity, B = acceleration 
D) A = position, B = velocity, C = acceleration

Quizplus · Accepted Answer

The position graph (s) is continuous and increases linearly with time, which means the velocity (v) graph is also continuous but is a straight horizontal line since the object is moving at a constant velocity. Therefore, graph B must be the velocity graph.

The acceleration (a) graph can be determined by looking at where the velocity is changing. From t=0 to t=2, the slope of the velocity graph is negative, indicating the object is slowing down, thus the acceleration must be negative during this time period. From t=2 to t=3, the velocity graph is a straight line with a slope of zero, indicating the object is moving at a constant velocity and the acceleration is zero. From t=3 to t=4, the slope of the velocity graph is positive, indicating the object is speeding up, thus the acceleration must be positive during this time period. Therefore, graph C must be the acceleration graph.

This leaves graph A to be the position graph, which makes sense since it is increasing with a constant slope.

The Graphs Show the Position s\mathrm { s }s , Velocity v=ds/dt\mathrm { v } = \mathrm { ds } / \mathrm { dt }v=ds/dt

The Graphs Show the Position $\mathrm { s }$ , Velocity $\mathrm { v } = \mathrm { ds } / \mathrm { dt }$